No, it is not true for all scenarios.
This idea was examined by Britney Gallivan, who came up with a mathematical model for the limits, and used this knowledge to fold a large piece of paper twelve times in January 2002.
She was a junior in high school at the time.
Reference: Historical Society of Pomona Valley
According to the above reference, the upper-bound equation for "Alternate Direction Folding", which I understand to be the normal style, is
Without LaTeX, this looks like:
W = πt.2^(3(n-1)/2)
Solve for n, we get:
n = 1 + 2/3.log2 (W/πt)
Plugging in the values for standard A4 80 g/m² office copy paper (W=297mm, t=0.105mm) we get:
n = 1 + 2/3.log2(297/(0.105π))
n = 7.543
- The equation works with square paper, and I have used A4's longest side, perhaps overestimating the number of folds by a fraction.
- The thickness of 80 g/m² was interpolated from the chart on cited page.
- Pi looks like this, in this font: π
If the original formula calculated by Gallivan is correct, this shows that a standard piece of copy paper, even if it is extended a little, cannot be folded 8 times.